A Sybil attack occurs when an adversary controls multiple system identifiers (IDs). Limiting the number of Sybil (bad) IDs to a minority is critical for tolerating malicious behavior. A popular tool for enforcing a bad minority is resource burning (RB): the verifiable consumption of a network resource. Unfortunately, typical RB defenses require non-Sybil (good) IDs to consume at least as many resources as the adversary. We present a new defense, ERGO, that guarantees (1) there is always a bad minority; and (2) during a significant attack, the good IDs consume asymptotically less resources than the bad. Specifically, despite high churn, the good-ID RB rate is O(TJ+J), where T is the adversary's RB rate, and J is the good-ID join rate. We show this RB rate is asymptotically optimal for a large class of algorithms, and we empirically demonstrate the benefits of ERGO.